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The $C^*$-algebras of quantum lens and weighted projective spaces

Tomasz Brzeziński, Wojciech Szymański, Tomasz Brzezinski Orcid Logo

Journal of Noncommutative Geometry, Volume: 12, Issue: 1, Pages: 195 - 215

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.4171/JNCG/274

Abstract

It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of contin...

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Published in: Journal of Noncommutative Geometry
ISSN: 1661-6952
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa37050
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first_indexed 2017-11-24T15:39:21Z
last_indexed 2020-07-14T13:03:20Z
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spelling 2020-07-14T11:24:51.5454074 v2 37050 2017-11-24 The $C^*$-algebras of quantum lens and weighted projective spaces 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2017-11-24 SMA It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2n+1q and the cyclic group ℤN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(ℙnq(m0,…,mn)), interpreted as fixed points under the circle action on C(S2n+1q), are computed under a mild assumption on the weights. Journal Article Journal of Noncommutative Geometry 12 1 195 215 1661-6952 Quantum lens space; graph algebra 23 3 2018 2018-03-23 10.4171/JNCG/274 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-07-14T11:24:51.5454074 2017-11-24T13:07:51.9926568 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzeziński 1 Wojciech Szymański 2 Tomasz Brzezinski 0000-0001-6270-3439 3 0037050-24112017131039.pdf lens.pdf 2017-11-24T13:10:39.1530000 Output 387587 application/pdf Accepted Manuscript true 2017-11-24T00:00:00.0000000 true eng
title The $C^*$-algebras of quantum lens and weighted projective spaces
spellingShingle The $C^*$-algebras of quantum lens and weighted projective spaces
Tomasz Brzezinski
title_short The $C^*$-algebras of quantum lens and weighted projective spaces
title_full The $C^*$-algebras of quantum lens and weighted projective spaces
title_fullStr The $C^*$-algebras of quantum lens and weighted projective spaces
title_full_unstemmed The $C^*$-algebras of quantum lens and weighted projective spaces
title_sort The $C^*$-algebras of quantum lens and weighted projective spaces
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzeziński
Wojciech Szymański
Tomasz Brzezinski
format Journal article
container_title Journal of Noncommutative Geometry
container_volume 12
container_issue 1
container_start_page 195
publishDate 2018
institution Swansea University
issn 1661-6952
doi_str_mv 10.4171/JNCG/274
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2n+1q and the cyclic group ℤN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(ℙnq(m0,…,mn)), interpreted as fixed points under the circle action on C(S2n+1q), are computed under a mild assumption on the weights.
published_date 2018-03-23T03:46:33Z
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score 10.999161

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